Large Covariance Estimation for Compositional Data Via Composition-Adjusted Thresholding

原文摘要

Yuanpei Caoa, Wei Linb & Hongzhe Lia*a Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PAb School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, ChinaCONTACT Hongzhe Li hongzhe@upenn.edu Department of Biostatistics and Epidemiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104.Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.ABSTRACTHigh-dimensional compositional data arise naturally in many applications such as metagenomic data analysis. The observed data lie in a high-dimensional simplex, and conventional statistical methods often fail to produce sensible results due to the unit-sum constraint. In this article, we address the problem of covariance estimation for high-dimensional compositional data and introduce a composition-adjusted thresholding (COAT) method under the assumption that the basis covariance matrix is sparse. Our method is based on a decomposition relating the compositional covariance to the basis covariance, which is approximately identifiable as the dimensionality tends to infinity. The resulting procedure can be viewed as thresholding the sample centered log-ratio covariance matrix and hence is scalable for large covariance matrices. We rigorously characterize the identifiability of the covariance parameters, derive rates of convergence under the spectral norm, and provide theoretical guarantees on support recovery. Simulation studies demonstrate that the COAT estimator outperforms some existing optimization-based estimators. We apply the proposed method to the analysis of a microbiome dataset to understand the dependence structure among bacterial taxa in the human gut.

摘要来源：OpenAlex